This article is cited in 2 papers

On Stability of Small Periodic Solutions

V. V. Abramov

Ryazan State University named for S. A. Esenin

Abstract: In this paper, we consider normal time-periodic systems of ordinary differential equations whose right-hand sides smoothly depend on phase variables and small parameters. Conditions of branching of small periodic solution of the system are found. Stability tests for small Lyapunov solutions with respect to parameters or variables are established. Our reasoning is based on the analysis of the first nonlinear approximation of the monodromy operator.

Keywords: system of ordinary differential equations, small parameter, monodromy operator, branching of a periodic solution, stability.

UDC: 517.925.51

MSC: 34C23, 34C25, 34D99

 English version: Journal of Mathematical Sciences (New York), 2020, 248:4, 375–381

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